For the sake of predictable variables, let's say this is the 2014 version of legendgoji vs shin's 4th form. That means legendgoji has the flame-like breath instead of the more beam-like version in KotM, and doesn't have any other KotM abilities. Meanwhile, let's assume that shin doesn't have time to evolve into a specialised anti-Godzilla form.

Personally, I think it's a tough one to call. Shin has the advantage at a distance, since his photon beam has much longer range than legendgoji's flame. The question is whether shin's beam could penetrate legendgoji's skin and do significant damage. Up close, legendgoji's brawler physique and greater agility would seem to give him the advantage over shin's weedy arms, but there's that huge tail to consider. Then there's endurance: both seem to take a similar amount of damage before being knocked unconscious, but what does it take to actually kill them?

I know how powerful the 2014 Godzilla is. I know next to nothing about Shin Godzilla. Shin would have a hard time defeating the 2014 one. I don't know if the 2014 one could defeat Shin easily. I believe that the two creatures won't be easy to kill. If there was away to kill them, I don't know what will work. That is what I think.